The following write-up summarizes messages about teaching math that I took away from some of the presentations.

Dr. Carol S. Dweck

As noted near the end of my Mindsetblog, many students have given up on math because they believe they are not good at math, and will never “get” math.

Teachers and parents are supporting a fixed mindset when they tell students, “Don’t worry, not everyone is good at math.” This kind of feedback writes kids off, gives kids lower confidence that they could ever do it, releases them from the responsibility of ever doing well in math.

On the other hand, teacher who are developing a growth mindset would say, “Let’s break this down even further and try some strategies together to see how you can get better.” When teachers and students believe skills can be developed, it opens students up to learning.

The highlight of my day definitely was meeting Dr. Carol Dweck in person. I got to tell her about our Learning Services’ team’s Mindset book study, how we involved ourselves in examining our mindsets, as individuals and as a team, and how we continually reflect on our growth.

Dr. Rafael Núñez

Dr. Núñez’ presentation worked to uncover the topic, “Where does math come from; making sense of human ideas.”

“Mathematics is a paradoxical conceptual system.”

Math concepts are not directly perceivable through the human senses. For example, we cannot see infinity…

Mathematical entities are imagined by humans, not visible in our environment, so how can we make sense of them?

Can we relate mathematics to other kinds of perception? If we can, maybe we can use those relationships to help us teach math. Conceptual metaphors help fictive motions make human imagination possible.

Metaphors– For example we can perceive the domain from a cold heart to a warm heart, so maybe numbers are also perceived as a domain, as if they have a location in space.

Fictive motion– “We often talk effortlessly about static objects as if they were moving.” For example, “The fence stops after the tree.” The conception we construe in that the fence is moving may provide the inferential structure required to conceive mathematical functions as having motion and directionality.

Gestures– we use hand and body gestures to enhance communication; to help the speaker express him/herself, which in turn, help the listener make meaning. Perhaps the intentional use of relevant gestures in teaching mathematics could support students in construing meaning as well.

Are there any mathematics that are hard-wired- the basic number line perhaps? Is this an embedded part of the brain, or something we need to learn? Núñez’ Yupno Study concluded that mapping a number to a point in space doesn’t come naturally-it seems that something as simple as a number line is not inherent, it is learned, and so, we need to intentionally teach it. If this basic simple model in math is not understood, concepts that depend its understanding will not be understood.

Núñez’ summarized his message by saying that “the portrait of mathematics has a human face”; articulating meaning is necessary because mathematics is such a complex conceptual system.

Also, like development along a continuum, the understanding of mathematical concepts relies on the understanding of previous concepts. If we do not understand what comes before, we will not understand what comes after.

Diane Chang

Diana is the Program Coordinator of the Robertson Program for Inquiry-based Teaching. During her presentation, Diana shared the “Math for Young Children: A Lesson Study Research Project” that she is working on. The driver behind this project is current research showing that success in early math skills are a better predictor of success in later years, than success in early literacy skills.

The lesson study involved a step-by-step approach.

With the support of facilitators, teachers did a lot of reading and professional learning about some key concepts in mathematics. They then chose a topic they wanted to focus their work on.

Students’ strengths and needs were assessed in this chosen topic. Teachers interviewed students and got them to work on some activities to see where their development was at in that concept area.

Based on the findings from the work with students, the team of teachers and facilitator co-designed exploratory lessons to help students develop their skills and overcome some misconceptions. During the exploratory lessons, the teachers observed each other’s students.

After debriefing to determine explicitly what needed to be taught to move the students forward in their development, the teachers built “public lessons” that they would all teach.

Teachers taught the public lesson.

Teachers debriefed the lesson and determined next steps.

The “public lessons” the teachers co-developed, as well as a summary of the Lesson Study can be found on Math for Young Children space on the Trent Math Education Research Collaboration website.

Why do we Resist the Evidence?

At the end of the day, the presenters assembled as a panel to address questions from the audience. A question one person asked was, “Why do we resist the evidence- why do we ignore the research and continue to use teaching methods that are not always the most effective?” Should we not embrace new evidence just as we embrace the dawning of a new day?

The panel offered several indirect responses to the question, and I also have some theories of my own, but I’d love to hear your response to the question, “…so why DO we resist the evidence?”

Hi Diane – The comments about mindset and math are so true. I’ve heard that for years and found a great response from my son’s math teacher at parent teacher interviews this week. Mr. T said that my son can read for understanding in LA, Social and Science, he must have the skill to read for understanding in math. When I shared that with my son adding that it would just take some practice, he brightened up and we’re doing math homework over spring break. It is all about Mindset! Great post!